mapping geometric shapes on surfaces with little distortion
I would use the UV Project modifier.

On the backdrop object just add the modifier.  You need to fill out three things (and make sure to check the Override Image option). 


The image
The uv map (does not have to be a pretty UV map, you just need the slot)
The projector object. If you use a camera or a spot light as the projector the Scale values will control the size of the texture. For any other type of object they do nothing, the object scale controls the size.




The node to render this are the same as you would use for any image. The modifier is changing the UV map so the image gets rendered "projected." 


It works really well (identically to how building projection works) which means you also get the real life "problems," off angle viewing will break the illusion. Also the focal length of the camera makes a difference (it will look perfect with an orthographic camera.)